science and engineering encyclopedia

Skew

An expression of the so-called "third moment". A tendency for a distribution to lean to the right (or left, when negative), showing a fast dip from the central mean but having an extended tail. The skewness of data is usually measured through a coefficient of skewness which is zero for symmetric distributions such as the normal or uniform distribution, is greater than zero for positively skewed data, and is less than zero for negatively skewed distributions. To judge whether data departs significantly from a normal distribution, a standardized skewness statistic can also be computed.

where

σ = standard deviation of x

N = total number of values of x

= mean of x

Standardized Skewness

A standardized form of the skewness statistic which renders the statistic free of scale. Standardized skewness can be used to test whether your data comes from a normal distribution. If it does, the statistic will fall between -2 and +2 about 95% of the time.